dmdt=ṁin−ṁout+ṁleak_in−ṁleak_out+ṁoild m over d t end-fraction equals m dot sub i n end-sub minus m dot sub o u t end-sub plus m dot sub l e a k _ i n end-sub minus m dot sub l e a k _ o u t end-sub plus m dot sub o i l end-sub ṁinm dot sub i n end-sub ṁoutm dot sub o u t end-sub are flow rates through the suction and discharge ports. ṁleakm dot sub l e a k end-sub accounts for clearances. ṁoilm dot sub o i l end-sub

Minor clearances along the sealing lines. Flow Equations

Further improvements require dynamic mesh CFD and coupled thermal analysis of rotors and casing.

Where $h_dis,is$ is enthalpy after isentropic compression to discharge pressure.

The working chamber is treated as an open thermodynamic system (control volume). The governing equations are derived from the conservation laws of mass and energy.

This is where simple models fail. Screw compressors have 5 internal leakage paths (blow-hole, sealing line, rotor tip, etc.).

is calculated by integrating the cross-sectional area of the fluid pockets along the axial length of the rotors:

[High Pressure Chamber] / | \ Interlobe Tip Blow-hole (Leakage Paths) \ | / [Low Pressure Chamber] Flow Calculations